Transport of Molecules in the Tumor Interstitium: a Review1

[CANCER RESEARCH 47. 3039-3051. June 15, 1987]

Review Transport of Molecules in the Tumor Interstitium: A Review1

Rakesh K. Jain Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890

Abstract these two spaces. We have recently summarized our work on blood flow and exchange in the tumor vascular subcompartment The transport of fluid and solute molecules in the interstitium is elsewhere (8, 9). In what follows we will discuss our own governed by the biological and physicochemical properties of the inter findings on the interstitial transport in tumors as well as those stitial compartment as well as the physicochemical properties of the test molecule. The composition of the interstitial compartment of neoplastic of others. tissues is significantly different from that of most normal tissues. In The transport of a solute or a fluid molecule in the intersti general the tumor interstitial compartment is characterized by large tium is governed by the physiological (e.g., pressure) and phys interstitial space, high collagen concentration, low proteoglycan and icochemical properties (e.g., size, charge, structure, composi hyaluronate concentrations, high interstitial fluid pressure and flow, tion) of the interstitial subcompartment as well as physicochem absence of anatomically well-defined functioning lymphatic network, high ical properties of the test molecule. These properties have been effective interstitial diffusion coefficient of macromolecules, as well as recently reviewed for normal tissues by several authors (10-15). large hydraulic conductivity and interstitial convection compared to most In this article we will discuss the tumor interstitial properties normal tissues. While these factors favor movement of macromolecules in the following order: volume, structure, and composition of in the tumor interstitium, high interstitial pressure and low microvascular the interstitial space (Section II); pressure-flow relationship in pressure may retard extravasation of molecules and cells, especially in large tumors. These differences in transport parameters have major the interstitium (Section III); and interstitial transport param implications in tumor growth and mÃ©tastases,as well as in tumor detection eters (Section IV). For each parameter, we will outline the and treatment. methods of measurement, discuss the key results, and finally point out the implications for tumor growth, detection, and I. Introduction treatment. Most normal and neoplastic tissues can be divided into three subcompartments: vascular, interstitial, and cellular. In addi II. Volume, Structure, and Composition of the Tumor Interstitial tion, most normal tissues also contain lymphatic channels in Space the interstitial compartment. Once a molecule used for cancer The interstitial subcompartment of a tumor is bounded by detection or treatment is injected into the blood stream, it encounters the following "resistances" before reaching the in- the walls of blood vessels on one side and by the membranes of cells on the other. In normal tissues, the blood vessels are tracellular space: (a) distribution through vascular space; (b) surrounded by a basement membrane, which may be damaged transport across microvascular wall; (c) transport through in or missing in tumors (for review see, e.g., Ref. 8). In addition, terstitial space; and (antigen) involved in growth, detection, or treatment (1-4). structure are the interstitial fluid and macromolecular constit Most investigators to date have focused their research on uents (hyaluronate and proteoglycans) which form a hydrophilic understanding the biochemistry, biophysics, and molecular bi gel. It is sometimes convenient to divide the interstitial space ology of cancer cells with limited attention paid to the in vivo into two compartments: the colic ;d-rich gel space containing interstitial environment they exist in. The advent of hybridoma the hydrophilic hyaluronate and proteoglycans; and the colloid- technology and genetic engineering has led to large scale pro poor free-fluid space. In this paper, we will discuss quantitative duction of monoclonal antibodies and other biologically useful results on the volume and composition of each of these spaces. molecules. If these molecules are to be used clinically, methods must be developed to deliver them selectively to the target cells in vivo (5-7). Since no molecule can reach the tumor cells from A. Volume of Interstitial Space blood without passing through the vascular and interstitial subcompartments, it seems reasonable to find out more about The volume of the interstitial space is usually obtained by the structure and function of these two subcompartments. We subtracting vascular space from the extracellular space. Vascu have focused our research in the past few years on the experi lar space is measured by a marker confined to blood vessels, mental and mathematical characterization of transport through and the extracellular space is measured by a marker excluded by cells. In a limited number of studies, these spaces have been Received 10/7/86; revised 3/9/87; accepted 3/20/87. measured morphometrically. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in Shown in Table 1 are the data of Cullino et al. (17) for accordance with 18 U.S.C. Section 1734 solely to indicate this fact. various carcinomas and a sarcoma. These investigators used 1This article is based on research supported by grants from the National sodium, chlorine, or D-mannitol as an extracellular marker and Cancer Institute, the National Science Foundation, and the Richard K. Mellon Foundation and by an NIH Research Career Development Award (1980-1985) dextran 500 (M, ~375,000) as a vascular marker. [Note that and a Guggenheim Fellowship (1983-1984). dextran 500 may overestimate the vascular space due to some 3039 Downloaded from cancerres.aacrjournals.org on September 29, 2021. © 1987 American Association for Cancer Research. INTERSTITIAL TRANSPORT IN TUMORS

Table I Interstitial spaces of tumors vascular permeability in tumors and/or selective affinity of injected substances for tumor cells. HostRatHumanTumorFibrosarcoma space(%)52.6 4956VV256 Â±4.3Â°36.3 carcinomaH5123 Â±2.8"43.3 B. Collagen and Elastic Fiber Content carcinomaH3683 Â±1.1"50.6 Â±3.5Â°54.6 carcinomaNovikofT Histological examination of tissues using appropriate stains hepatomaNormal Â±4.4Â°20.5 liverGastrocnemius Â±0.6Â°15.6 demonstrates the presence of collagenous and elastic fibers. The muscleDS-carcinosarcomaSarcoma-MSarcoma-BSkeletalÂ±0.7Â°38Â»40eSff13C60 basic structural unit of the collagenous fibers is the collagen molecule. The main body of this protein molecule has a cylin drical structure (diameter, ~ 1.5 nm; length, ~300 nm; molec muscleFibrosarcoma ular weight, ~285,000) and is composed of 3 peptidic a chains A-MCFibrosarcoma Â±555 (molecular weight, ~95,000) coiled in a rope-like fashion to C-MCFibrosarcoma Â±I3314 BP-IIMuscleSkinLungKidneyGliomasMeningiomasNormal form a triple helix. Depending upon the composition of the a Â±234 chains, the collagen molecules can be divided into at least 10 Â±329 Â±834Â±620-40*13-15Â»6-7*Ref.1718192021types; each type has similar structure and size (23). While the collagen fibers offer considerable tensile strength along their length, elastic fibers provide the rubber-like elasticity to a tissue. The structural units of elastic fibers are the microfibrillar pro brainInterstitial tein and elastin. The physical and mechanical properties of ' Interstitial space: mean Â±SD; tumor weight, ~2-15 g; sodium, chlorine, or elastic fibers depend on their amino acid composition (14, IS, i>nKinniicilas extracellular marker and dextran 500 as vascular marker. * Extracellular space; morphometric analysis. 23). *Extracellular space; tracer, "Cr-EDTA; measurement made ~50 min postin Collagen is usually measured by tissue content of hydroxy- jection. proline, since it is assumed that this amino acid occurs almost exclusively in the scleroproteins of the connective tissue (24). Collagen content of nine hepatomas, W256 carcinoma, R-2788 extravasation (8).] The interstitial space of tumors in general is lymphosarcoma, and two fibrosarcomas in rats and two hepa very large, and that of hepatomas is more than twice that of the tomas in mice was measured by Cullino et al. (24-26). All host liver. Similar results were obtained by Rauen et al. (18), Appelgren et al. (19), and O'Connor and Bale (20) in various hepatomas contained more collagen than liver did (Table 2). Unlike regenerating liver, collagen content per unit tissue sarcomas and by Bakay (21) in human brain tumors (Table 1). weight remained constant during growth in eight of nine rat Although implications of the large interstitial space are not hepatomas. In Hepatoma 5123, during growth, collagen con completely understood, it seems reasonable to assume that the tent per unit tissue weight decrease was similar to that for large "free-fluid" space would offer less resistance to interstitial regenerating liver. The results shown in Table 2 do not agree transport (22). In addition, this large space would serve as a with those of Grabowska (27) who found a rapid decrease in "sink" or a "reservoir" for substances injected into the body collagen content of Guerin rat carcinoma and sarcoma as the (2). The large amount of blood-borne substance accumulated in tumor grew to 1.5 g. However, the collagen content per unit this space may also give an erroneous impression of increased weight remained constant between 2 and 30 g tumor weight,

Table 2 Collagen content of hepatocarcinomas and liver"

(mg/100 Strain/sexHepatocarcinomas*Rat denominationNovikoffLC1836833924AT3-2HCLC35123129 Gig/mgN)10.9 mg protein)1.301.302.063.693.825.042.464.344.341.062.302.162.051.021.061.010.680.630.39

linesSprague-Dawley (M)Fisher-344 Â±14.6Â°2.9 Â±0.810.9 (F)AxC(F)A Â±6.23.3 Â±0.517.4 Â±9.02.2 Â±0.630.5 X C(F)Buffalo Â±7.44.2 Â±1.832.4 (M)OM(M)OM(F)OM(F)Buffalo Â±11.14.0 Â±1.242.6 Â±7.83.9 Â±2.020.9 Â±6.63.5 Â±1.328.1 Â±7.83.4 Â±2.036.6 (M)Mouse Â±9.60.75 Â±2.08.9

linesC3H (M)C3H solid129 Â±3.60.40 Â±0.519.7 (M)C3H ascites134 Â±1.40.60 Â±1.318.2 (F)C3H solid1 Â±2.10.60 Â±1.117.3 (F)Normal 34ascitesNormalNormalNormalNormal14 Â±1.5190-210Â°'130-145180-200190-210190-210190-210HydroxyprolineÂ±0.88.6

liverRat linesSprague-Dawley (M)Fisher Â±0.49.0 344(F)A Â±0.28.5 x C(F)Buffalo Â±0.15.9 (M)Sprague-Dawley Â±0.25.3 (M)Buffalo daysregenerating14 Â±0.33.4 (M)Tissue days regeneratingWt(g)4.1 Â±0.2Collagen Â°From Cullino et al. (24, 25); reproduced from paper of Cullino (16) by permission. * Additional information in the paper of Cullino and Grantham (26). c Mean Â±SD. * Host weight. 3040 Downloaded from cancerres.aacrjournals.org on September 29, 2021. © 1987 American Association for Cancer Research. INTERSTITIAL TRANSPORT IN TUMORS similar to Gullino's findings. Cullino et al. (24) attributed the charide fragments and may ultimately affect the immune re initial reduction in collagen content of tumors to the inability sponse of the host (16). The data on HA bound to the collagen of Grabowska's technique to separate the small tumor from the matrix in tumors are not available. collagen-rich s.c. tissue. Unlike hyaluronate, the data on the proteoglycans (GAG) Cullino and Grantham (25) demonstrated that the tumor content of tumors are limited. Boas (37) and Pearce (38) found collagen is produced by the host and its synthesis is governed hexosamine content in mouse s.c. tissue to be â€”0.18% and by the tumor cells. These authors also showed that collagen -0.14%, respectively. Brada (39) measured it to be -0.027% in content per unit tumor weight remains constant in all transplant both Ehrlich and Krebs tumors in mouse. In contrast, Sylven generations regardless of site or age of tumors. If tumor growth (40) found relatively high GAG content in various sarcomas depends on collagen production to the extent that it depends (0.1-1.5%). Since in Sylven's investigations GAG content was on neovascularization, this characteristic of tumors may be measured in the fluid collected by blunt dissection and forma exploited in arresting the tumor growth. However, this author tion of small pouches in the tissues, the validity of results is not aware of any such attempts. depends upon the extent of damage done to the tissue/cells. Unlike collagen, no attempt has been made to quantify the Due to the importance of these macromolecules in the solute elastic fiber content of tumors. These fibers account for -2- and fluid transport in tumors, a definite need exists to measure 5% of the dry weight of skin (28) and -30-60% of the elastic their concentrations in various tumor types. arteries (e.g., aorta) (15). Due to internal structure of collagenous and elastic fibers, D. Composition of Tumor Interstitial Fluid these fibers have water space within them which is probably accessible to small molecules and ions (e.g., glucose, urea, Methods. The results on interstitial fluid composition are sodium, and chlorine). The water contents of collagenous and controversial due to the methodological problems as well as the elastic fibers are estimated to be -0.6 ml/g collagen and -0.56 heterogeneity in the interstitium. Most commonly used meth ml/ml elastin, respectively (15, 29, 30). The implication of this ods include: direct sampling using needle (catheter) or micro space in interstitial transport is not understood. pipet; implanted wicks; and chronically implanted micropore chamber (or perforated capsule) technique. [All of these tech niques were originally developed for interstitial pressure meas C. Polysaccharides urements (see Section 111A).]The major problem with the direct sampling method is the cellular and vascular damage caused by Various in vitro and in vivo studies have shown that the stabilized polysaccharide network (hyaluronate and proteogly- puncturing the tissue; as a result the fluid collected may be a mixture of cellular and pericellular fluids. Although micropipets cans) enmeshed in the collagenous fibers offers considerable may reduce this damage, one is not sure whether the fluid resistance to interstitial transport. While the insoluble fibrous withdrawn represents the free-fluid phase or the gel phase. proteins (collagen and elastin) impart structural integrity to a Furthermore, the applied suction may increase net capillary tissue, the polysaccharides are though to govern the mass filtration and lower interstitial fluid concentration. The major transfer characteristics of the tissue due to their high negative objection to the wick technique is that it may act as a colloid charge density and hydrophilic character. The mutual repulsion osmometer. Finally, the major objections to the chamber/cap of negative charges on the chains leads to swelling in solution. sule procedure are: (a) the chamber may influence the structure In addition, these polysaccharides impart viscoelastic behavior of the surrounding tissue; and (b) the chamber fluid may not to the interstitium. The viscosity of the polysaccharide solutions represent interstitial fluid due to hindered transport across the depends upon their molecular weight, pH, and binding between micropore membrane or the surrounding connective tissue hyaluronate and proteoglycans and/or other tissue components. layer. Cullino Ã©tal.(41)presented the following data in support (For detailed review, see e.g., Refs. 23, 31, and 32.) of the use of their chamber for TIF measurement: (a) the pore Choi et al. (33) have reported hyaluronate content of 0.018% size (0.45 /JIN)is large compared to the molecules present in in a rat chondrosarcoma. ToÃ³leet al. (34) reported hyaluronate the TIF; (Â¿>)samples collected outside and inside a chamber contents of 0.014 and 0.028% in a carcinoma and s.c. tissue of immersed in plasma have identical compositions; (<â€¢)whentwo a nude mouse. In contrast, these authors found unusually high chambers are placed close to each other in a s.c. pouch or a content of hyaluronate in V2 carcinoma in rabbits and attrib uted it to its metastatic properties. Fiszer-Szafarz and Cullino tumor, proteins with enzymatic activity placed in one chamber (35, 36) studied the relationship between HA2 and hyaluroni- can be found in the other chamber; and (d) histolÃ³gica! exam ination shows neoplastic cells touching the chamber (16, 42, dase in the interstitial fluids of tumor and the s.c. tissue (TIF 43). There are three problems with this chamber which should and SIF, respectively). They found HA concentration of SIF to be kept in mind: (a) implant of the chamber in the s.c. area be 53.5 Mg/ml fluid in the scapular region, but only 37.2 ng/m\ leads to lactic acid production from glucose in -1 week to -1 in the lumbar region. In W256 carcinoma HA concentration month and formation of a fibrosarcoma in -1 year; (b) it takes was 38 Mg/ml when grown in the scapular region and 20 Mg/ml several days to fill up the chamber and hence it has a slow when grown in the lumbar region. Further, the concentration dynamic response; and (<â€¢)theability of this chamber to measure of HA was -25% lower in s.c. areas distant from the tumor. the exchange of macromolecules has not been tested independ These investigators attributed the low HA concentration in ently, especially in light of hindered diffusion offered by the tumors to the concomitant elevated TIF hyaluronidase activity, which was -57% higher in TIF than in SIF. The increased connective tissue layer around the chamber. hyaluronidase activity may make tumors a source of polysac- Other procedures for sampling the interstitial fluid include: (a) sampling the lymph fluid [Note that the equality between 1The abbreviations used are: HA, hyaluronic acid; GAG, glycosaminoglycans; interstitial free fluid and lymph is still unresolved (15).]; (Â¿>) MP, micropipet technique; TIF, SIF, NIF, tumor, s.c., and normal interstitial determination of solute concentration in excised tissues; (c) fluid, respectively; IFP, interstitial fluid pressure; TIFP, SIFP, pressure of TIF and SIF, respectively; BSA, bovine serum albumin; WIN, wick-in-needle tech intravital fluorescent microscopy; and (d) exchange kinetics of nique; IF, interstitial fluid; 0, value in water. radiolabeled solutes. The advantages and disadvantages of each 3041 Downloaded from cancerres.aacrjournals.org on September 29, 2021. © 1987 American Association for Cancer Research. INTERSTITIAL TRANSPORT IN TUMORS Table 3 Composition of interstitial fluid of tumors" compared with serum, lymph, and peritoneal fluid

of blood of blood inter efferent from afferent to tu from s.c. in stitialfluid3.2 tumor5.2 mor4.8 thoracicduct2.5 terstitialfluid4.1 Total proteins Kin ml Â±0.1' Â±0.2 Â±0.1 Â±0.2 Â±0.1 Â±0.3 Â±0.2 Free amino-N mg/100ml 5.9 Â±0.4 5.1 Â±0.2 5.2 Â±0.2 6.3 Â±0.4 4.0 Â±0.2 5.5 Â±0.2 6.3 Â±0.2 Free glucose mg/100 ml Traces 123 Â±6 188 Â±8 108 Â±6 Traces 125 Â±5 105 Â±12 Lactic acid mg/100 ml 161 Â±11 122 Â±4 90 Â±8 20 Â±3 158 Â±10 27 Â±4 28 Â±4 Total cholesterol mg/100 ml 8Â±2 64 Â±5 60 Â±4 28 Â±3 22 Â±4 150 Â±9 29 Â±4 Lipid phosphorus mg/P 100 ml 1.1 Â±0.1 5.0 Â±0.3Serum 5.0 Â±0.3 0.8 Â±0.1fluidAscites*321.0 + 0.1 4.9 Â±0.4Normal 2.0 Â±0.8 DensityUnitsK g/mlTumor 1.014Serum 1.019PeritonealNormal3.8 1.017Lymph 1.014 ' All data from Walker carcinoma 256 and Sprague-Dawley rats except those under "Ascites." Reprinted from paper of Cullino (42) with permission of S. Karger AG, Basel. * Data from Hepatoma 7974 in Japanese/N rats (44). ' Mean Â±SD.

of these techniques are discussed by Aukland and Nicolaysen LymphaticVesselt1 (12). Results. According to Starling's hypothesis, the driving force for transcapillary exchange of fluid is the difference between intra- and extravascular hydrostatic and osmotic pressures. Because of their low reflection coefficient and high permeabil |1tArterial ity, most low molecular weight solutes do not contribute signif SpaceVessel icantly to the osmotic pressure gradients, at least at steady state. Concentrations of various low molecular weight solutes (e.g., â€¢-l11Venou ions, nutrients, waste products, and enzymes) have been mea EndInterstitBloodal End sured by Cullino et al. (41, 42) in TIP, SIF, and plasma and are summarized in Table 3. TIP has high H+, CO2, and lactic Fig. 1. Schematic of solute and fluid movement in the normal interstitial space. Solute refers to macromolecules and fluid refers to dilute solution of small acid concentrations and low glucose and O2 concentrations as hydrophilic molecules in water. Note that transcapillary nitration and reabsorp- compared to SIF. The differences in the concentrations of H+, tion of fluid depend upon the hydraulic and osmotic pressure differences between intravascular and extravascular spaces, per Starling's hypothesis. The small CO2, glucose, lactic acid, cholesterol, lipid phosphorus content, amount of fluid which is not reabsorbed is collected by the lymphatic vessels. and free amino acids between plasma and TIF are significant, Movement of fluid through the interstitium and into the lymphatic vessels results perhaps due to tumor metabolism (see also Ref. 45). from relatively small shifts in hydraulic and osmotic pressure gradients. Move ment of macromolecules is due to diffusion as well as convection associated with Based on the invasive characteristics and presence of necrotic fluid motion. Since anatomically well-defined, functioning lymphatic vessels may areas in tumors, it is generally assumed that TIF has high levels be absent in a neoplastic tissue, the excess fluid and macromolecules ooze out of of proteolytic and lysosomal enzyme activities. The experimen the tumor and may be collected by the lymphatic vessels of the surrounding tal data on this subject are inconclusive. Sylven et al. (46-49), normal tissue. using the direct sampling method, have shown increased lyso somal and proteolytic activity in TIF, especially in necrotic tissue. According to the hypothesis of Starling (53), fluid move areas. Cullino and Lanzerotti (50) have also reported increased ment across the vessel wall is governed by the transcapillary activity of six lysosomal enzymes during mammary tumor hydrostatic and osmotic pressure gradients. Most of the fluid regression (which involves digestion of dead cells similar to filtered into the interstitial space is reabsorbed into the micro- necrosis); however, they found the increase in activity in the vascular network by the Starling mechanism. The residual fluid cells and not in the pericellular fluid, either before or during is taken up by the lymphatic vessels. Since tumors may not regression. In a separate study, Fiszer-Szafarz and Cullino (36) have anatomically well-defined lymphatic vessels, this residual did report increased activity of hyaluronidase in TIF. fluid may ooze out of the tumor periphery and may be reab The results on the protein concentration in TIF are as con sorbed by the lymphatics of the surrounding normal tissue thus troversial as in the NIF. Based on high effective vascular aiding lymphatic dissemination of cancer cells. If the fluid permeability and effective interstitial diffusion coefficient in reabsorption is not rapid enough and/or tumor cells continue tumors (8) one would expect higher concentrations of plasma to proliferate, the pressure in the interstitial space may increase. proteins in TIF than in NIF. In support of this hypothesis are This elevated pressure may lead to vascular occlusion and the data oi Sylven and Bois (47) who, using the direct sampling ultimately necrosis and/or may facilitate intravasation and ul method, found TIF and SIF concentrations, respectively, -67- timately vascular dissemination of cancer cells. The objective 97% and -30-50% of the plasma concentration (TIF, -3.9- of this section is to address these issues by examining the 5.7 g/100 ml; NIF, -2.8 g/100 ml) (see also Ref. 51). On the available data on the interstitial pressure and fluid flow in other hand, using the chamber method Cullino et al. (41) found tumors. (The implications of fluid flow in the solute transport opposite results (Table 3). These results are surprising espe are discussed in Section IV.) cially because extravascular deposition of fibrin is a prominent feature of neoplasia (52). Since a major fraction of the body's plasma proteins is found in the extravascular compartment and A. Interstitial Pressure in Tumors their concentrations in plasma and interstitial space govern transcapillary exchange, more work is needed on the composi Methods. Currently, there are three methods to measure local tion of interstitial fluid for both normal and neoplastic tissues. interstitial pressure, (a) needle, (b) WIN and (c) MP, and one method to measure average interstitial pressure, micropore chamber, also referred to as the perforated capsule method. III. Interstitial Fluid Pressure and Flow in Tumors Each of these methods has its advantages and limitations (see, The schematic shown in Fig. 1 depicts the current concept of e.g., Refs. 54 and 55 for detailed comparison). fluid and solute movement in the interstitium of a normal In the needle method, first used by Henderson in 1936, a 3042 Downloaded from cancerres.aacrjournals.org on September 29, 2021. © 1987 American Association for Cancer Research. INTERSTITIAL TRANSPORT IN TUMORS

Table 4 Â¡nlerstilalfluid pressure of tumor and host normal tissues Pressure (mm Hg) mean Â±SD Method and size of Host tissue (range) Ref. Host Tumor Age/size probe Host Tumor CHÂ° Rat W256 carcinoma 5-10g (7-9) (8-16) 41 H5123 H7974 Novikoff hepatocarcinoma Fibrosarcoma 4956

W256 carcinoma 3-5.1 g s.c. tissue (-0.1-+0.5) (6-22) CH 58

W256 carcinoma -1.3 g (5 Testis 2.98 Â±0.2 21.2 Â±4.1 N(26-gauge) 59 days)

DMBA-induced mammary ~0->5.5 g Skin -0.2 Â±1.2 (2.4 Â±2.4*- WIN (0.6 mm o.d.) 60 carcinoma (6-8 wk) 16.0 Â±4.8) MP (1-3 urn)

DMBA-induced mammary 3.4 Â±0.15 g Skin Not measured 10.3 Â±1.3 WIN (0.6 mm o.d.) 61 carcinoma (1.1-7.3 g)

MCA-induced sarcoma 0.25-1.7 g Tail 4.7 Â±1.4 26.6 Â±11.5 WIN (0.6 mm o.d.) 62 (12-35 days)

Hepatoma ascites (7-21 days) s.c. tissue â€”2.2 (-0-30) N 63 AH 109A AH 272

Rabbit Brown-Pearce carcinoma (-12 days) Testis 8.3 Â±1.3 19.3 + 6.0 N(21-gauge) 57

VX2 carcinoma 0.05-2 g (8- s.c. tissue -O (-2-20)' MP (1 Mm) Footnote 26 days) 3 " CH, micropore chamber, N, needle; o.d., outside diameter; DMBA, dimethylbenzanthracene; MCA, 3-methylcholanthrene. b Measured intratumor pressure gradients as a function of tumor size; see text for details.

needle filled with physiological saline coupled to a pressure- animal tumors using all four techniques (Table 4) and the results measuring device is inserted into the tissue, and pressure is agree with Young's findings (58-63). The increased value of increased until fluid flows into the tissue. The pressure at this TIFF has been attributed to the absence of a well-defined point is considered to be equal to the interstitial fluid pressure. lymphatic system in the tumor (58) and to increased permea In the wick-in-needle technique, a wick made of polyester or bility of tumor vessels (8). other fibers is placed in the needle to provide a large surface Young et al. (57), Wiig et al. (60), Paskins-Hurlburt et al. area continuum with the interstitium and to reduce occlusion. (59), Hori et al. (63), and Misiewicz and Jain3 have examined Both needle and WIN methods can cause tissue distortion and the intratumor pressure as a function of tumor size. All these trauma. Fluid injection in the needle technique may increase investigators found that as the tumor size increases, TIFF rises, interstitial pressure. The fibrous wick may act as a colloid presumably due to the proliferation of tumor cells in a confined osmometer in the WIN technique in chronic measurements. area as well as high vascular permeability and possible absence Micropipets, 1-3 urn in diameter, connected to a servo-null of functioning lymphatic vessels in tumors. This increase in pressure-measuring system reduce the problems of needle and TIFF also correlates with reduction in tumor blood flow and WIN techniques considerably. Most investigators have not been development of necrosis in a growing tumor (9, 59, 60, 63).' able to use this method for depths greater than 800 /Â¿mdueto Wiig et al. (60) attributed the rise in TIFF to ischemie cell pipet breakage. We have been able to overcome this problem swelling as well. by choosing suitable glass capillaries to make pipÃ©is.' Wiig et al. (60) and Misiewicz and Jain3 have also examined The micropore chamber technique was introduced at about the intratumor pressure gradients. Using the WIN technique, the same time independently by Guyton (56) and Cullino et al. Wiig et al. (60) found that in tumors <2.5 g, pressure in the (41) to sample the interstitial fluid of normal and tumor tissues, outer one-third of the tumor is 6.0 Â±1.7 (S.D.) mm Hg and in respectively. In this method, the chamber must be implanted in the central one-third it is 11.4 Â±4.1 mm Hg, whereas in tumors the tissue days in advance so that it is filled up with the >5.5 g, the values in these regions are 9.6 Â±3.5 and 16.0 Â±4.8 interstitial fluid by the time of measurement. As a result, this mm Hg, respectively. The highest TIFF measured was +23.3 method cannot be used for dynamic measurements. In addition, mm Hg in the central region of a tumor >5.5 g. Using the MP the connective tissue surrounding the chamber may act as a technique, these authors found TIFF equal to 2.4 Â±2.4 mm semipermeable membrane, excluding large molecules from the Hg in the superficial layer (<800 urn) of small as well is large chamber fluid and consequently introducing osmotic effects. tumors. Our results using the MP technique for the entire Cullino (43) has carefully examined several of these effects in tumor are in general agreement with tiiose of Wiig et al. (60) his studies of tumor pathophysiology and found them to be (Fig. 2). negligible. (See Section HD.) A limited number of investigators have attempted to modify Results. Young et al. (57) were the first investigators to TIFP with physical and chemical means. For example, Young measure TIFP and found it to be higher than IFF in the normal et al. (57) reported that IFF in both normal and neoplastic host tissue. Since that time IFF has been measured in several tissues increases by injection of fluid (0.5 ml) into the tissue 3M. Misiewicz and R. K Jain. Interstitial pressure gradients in VX2 carci and by the application of digital compression. This fact should noma, manuscript in preparation. be kept in mind during the diagnosis and treatment of human 3043

for a novel method of measuring convective velocity of a solute.) Tumor 3 V~ 1.87cm5 State ~ Necrotic Results. Hemoconcentration measurements by Butler et al. 10 (58) show that in four different mammary carcinomas, 2-5 g, the fluid loss, QtF, to the interstitial compartment is ~0.14- 0.22 ml/h/g tissue (Table 5). This is approximately 5-10% of Tumor 2 V~026 cm' plasma flow rate through these tumors and significantly more State ~ Viable than the lymph drainage in most normal tissues [0.0017-0.072 ml/h/g (12)]. The oozing out of this fluid from tumors may be responsible for the peritumor edema often seen in s.c. tumor Tumor 1 V-0.07 cm* implants and may play a role in the production of lymphatic State Â»Viable metastasis. Although the direction and magnitude of these convective currents were not measured by these investigators, Subcut Outer 1/3 Middle 1/3 Central 1/3 their results explain the observations of Reinhold (65) who found the spread of pyranine dye in tumor interstitium at rates Fig. 2. Interstitial pressure gradients in VX2 carcinoma. Note the increase in pressure as the tumor grows. From Misiewicz and Jain.3 faster than predictable by diffusion alone (66). Although convective flow depends on the pressure gradients tumors, e.g., palpation, especially if repeated or applied injudi and hydraulic conductivity of the medium (see Equation A), ciously; aspiration biopsy; and the local injection of anesthetics these authors found a significant correlation between Q,, and or other pharmacological agents. Similarly, Wiig and Gadeholt tumor blood flow rate per unit mass. Since tumor blood flow (62) were able to increase TIFP by increasing the venous rate per unit mass decreases as a tumor grows (for review, see pressure (which also resulted in skin and tumor blood flow Ref. 9), QIF was found to be proportionately less for large reduction) and by plasma volume expansion with 5% BSA tumors. It is worth noting here that these investigators found no difference in QIF in growing versus regressing hormone- solution (which also resulted in skin and tumor blood flow increase). Finally, Tveit et al. (61) reported a decrease in the dependent tumors (58). IFF of dimethylbenzenthracene-induced mammary carcinoma Continuous drainage of interstitial fluid from micropore chambers showed that tumors oozed out ~4-5 times more fluid in rats from 10.3 Â±1.3 mm Hg to 7.0 Â±1.1 mm Hg during than the s.c. tissue (~3.5-4.75 ml/day versus ~0.9 ml/day). noradrenaline infusion. This agent, which is a potent vasocon strictor, increased the systemic pressure by 30-40 mm Hg and Furthermore, the fluid drained from tumors in ml/day remained decreased tumor blood flow. These studies do not support the fairly constant as the tumor grew from 2 g to 26.5 g in 5 days hypothesis that reduction in tumor blood flow is a result of (58). increased TIFP. C. Theoretical Studies of Interstitial Pressure-Flow Relations Whatever the key factor or factors for the increase in TIFP are, absence of functioning lymphatic vessels, increased perme As discussed in Section II, the interstitial space is considered ability to macromolecules, tumor cell proliferation in a rela to have two compartments, the colloid-rich gel space containing tively rigid area, or ischemie cell swelling, the elevated TIFP the hydrophilic hyaluronate and proteoglycans at or near equi has profound implications in tumor growth, detection, and librium with the colloid-poor, free-fluid space. In this model, treatment. For example, increased TIFP may facilitate the the gel phase is considered to be immobilized, although the entrance of cancer cells into tumor blood vessels or into the possibility of mobile hyaluronate cannot be excluded (35, 36, surrounding normal tissue lymphatics, thereby aiding the met 67). In addition, whether these two compartments are arranged astatic process. Increased TIFP may reduce the Starling forces in series or in parallel is not known (15). Finally, although responsible for extravasation of fluid and various solutes, e.g., preferential fluid channels and rivulets have been reported in cytotoxic agents, monoclonal antibodies, biological response the interstitial space by Nakamura and Wayland (68) and modifiers, making it difficult to deliver these detection/treat Casley-Smith (69), to date no direct measurements of fluid ment agents to large tumors. Increased TIFP may also hinder velocity in the interstitium have been made. To this end, a extravasation of leukocytes involved in immune response. All limited number of investigators (e.g., ReÃs.70-72) have com these effects are also influenced by the microvascular pressure puted velocity and pressure profiles around single and multiple in tumors which has been found to be low compared to that in capillaries using Dairy's law for flow through a porous medium: the host tissue (64). (A) B. Interstitial Fluid Flow in Tumors Methods. Increased pressure gradients in the tumor intersti- where u is the fluid velocity, p is the pressure, and A, is the tium suggest the existence of significant convection in the tumor Table 5 Interstitial fluid loss in mammary tumors" interstitium. To measure this fluid flow, Butler et al. (58) MTW9* utilized two methods: (a) comparison of erythrocyte concentra Tumor DMBA NMU W256 Wt (g) (mean Â±SE) 4.3 Â±0.9 3.8 Â±1.0 2.3 Â±0.4 3.9 Â±0.6 tion (hematocrit) of tumor afferent and efferent blood in a Hc (mean Â±SE) 1.042 Â±0.006 1.068 Â±0.011 1.051 Â±0.013 1.029 Â±0.007 tissue isolated preparation where tumor is connected to the IF loss host by a single artery and a single vein (43); and (b) continuous ml/hr/gc 0.22 0.19 0.14 0.18 % blood perfused 4.2 5.1 2.7 6.7 drainage of the interstitial fluid from micropore chambers em % plasma perfused 6.5 8.5 4.5 10.2 bedded in normal and neoplastic tissues (43). " Data from Butler et al. (58). Note that both of these methods provide values of "net" * MTW9, hormone-dependent tumor, DMBA, NMU, chemically induced tu mors; W256, Walker 256 carcinoma; H, hematocrit of efferent blood/hematocrit interstitial flow (as measured by fluid loss), and not of the local of afferent blood (/' < 0.001); IF, interstitial fluid. convective velocity of the fluid. The latter has not been mea ' Values of lymph flow for normal tissues range from 0.0017 ml/h/g (human sured for normal or neoplastic tissues to date. (See Section IVA skeletal muscle) to 0.072 ml/h/g (rabbit intestine). (From Table 4 of Ref. 12.) 3044 Downloaded from cancerres.aacrjournals.org on September 29, 2021. © 1987 American Association for Cancer Research. INTERSTITIAL TRANSPORT IN TUMORS hydraulic conductivity. (See Section IV for measurements and Most methods require measuring solute flux at a known con values of K.) These theoretical analyses show large pressure centration gradient or measuring relaxation of concentration gradients near the capillary wall which die out at distances gradients as a function of time in the medium and then fitting beyond a few capillary diameters (71). [Note that in addition to the steady or the unsteady state diffusion equation to the small scale pressure gradients around individual capillaries, concentration data to extract the diffusion coefficient. large scale pressure gradients exist in tumors from its center to Due to the difficulties involved in measuring the concentra the periphery (Fig. 2). The relationship between these two tion gradients in the interstitial space in vivo, most diffusion pressure gradients has not been studied theoretically or exper measurements to date have been carried out in tissue slices /"// imentally.] These analyses also point out that the convective vitro or in various gels/solutions as a model of the interstitium. transport patterns in the interstitium are quite sensitive to Only recently have the developments in quantitative fluorescent intravascular pressures and intercapillary interactions (72). It microscopy allowed measurements of the effective interstitial must be mentioned here that these authors in their models diffusion coefficients in vivo (12, 22, 68, 75-81). There are assume fluid filtration and reabsorption to occur at the arterial three major problems with the intravital fluorescent microscopy and venous ends of capillaries, respectively. Zweifach and I i methods: (a) these methods can be used only for thin tissues or powsky (73) on the other hand propose that Filtration and for the superficial layer of thick tissues; (b) the effective diffu absorption are also temporal (periodic) processes not just spa sion coefficients include both diffusive and convective compo tial ones. The basis of their conjecture is that under normal nents; and (c) several biologically useful molecules, e.g., ().. conditions the interstitial colloid osmotic pressure is ~8-10 ('(),, are not fluorescent, and their molecular weight is less than mm Hg and the interstitial hydraulic pressure is ~0 mm Hg. that of currently available fluorescent tags. The first problem Direct pressure measurements suggest that the pressure drop across a 600-1200-fim path from pa-capillary to post capillary has been addressed by Goldstein et al. (82) who monitored transport in tumors using fiber optic microfluorometry; how is ~3-5 mm Hg. On the other hand, presumably due to arterial ever, poor spatial resolution and fluorescence quenching do not vasomotion, the pressure in capillaries fluctuates from as low as 10-15 mm Hg during near stasis to as high as 20-25 mm permit one to extract diffusion coefficient from their approach. Regarding the second problem, we have recently proposed the Hg above blood colloid osmotic pressure during maximal flow. use of fluorescent recovery after photobleaching to discriminate Experimental measurement of fluid velocity in the interstitium interstitial convection from diffusion in vivo (83). In this is now needed to resolve the temporal and spatial contributions method, which is used routinely by cell biologists, a well-defined to the fluid flow. concentration gradient of a fluorescent tracer is artificially IV. Transport Parameters Characterizing Interstitial Diffusion imposed in the extravascular region of a tissue by photobleach and Convection in Tumors ing with a laser beam. The relaxation of the concentration profile is monitored and analyzed to yield the diffusion coeffi Transport of molecules in the interstitium is due to concen cient and the convective velocity (83, 84). tration gradients (diffusion) and the motion of interstitial fluid When the diffusing species (e.g., O2, CO2, antibodies) binds (convection). For one-dimensional transport, the diffusive flux, J,,, of a solute in a medium is given by Fick's law: to or reacts with any component of the tissue, the estimation of its diffusion coefficient becomes even more complex. If reaction and binding are not properly accounted for, the values dC (B) of diffusion coefficients may be incorrect. One solution to this problem is to study transport of a nonreacting species which is where I) is the diffusion coefficient of the solute in the medium, similar in size, structure, charge, and configuration to the and dC/dx is the concentration gradient of solute (C is concen species in question. tration and x is position or distance coordinate). Similarly, the Results. Effect of Tissue Water Content. Vaupel (51) has convective flux, Jâ€žisgiven by: recently compiled the tissue diffusion coefficients of various small molecular weight species: O2, CO2, N2, H2, glucose, and Jc = CRpU = -CRfK -r (Q inulin (Table 6; Refs. 66 and 85-91). All D values presented were corrected to 37Â°C(310Â°K)by the following correlation where u is the convective flow velocity of the solvent resulting based on the Stokes-Einstein equation (74): from pressure gradients in the medium (see Equation A), RF is the retardation factor (solute convective velocity/solvent con />3,o= Dr-3*-- (D) vective velocity), A is the tissue hydraulic conductivity for convective flow of solvent through the medium (k/rÂ¡,where k is Darcy's constant, and r, is solvent viscosity) and dp/dx is the Table 6 Diffusion coefficient of glucose and inulin (cnf/s) pressure gradient (p-hydrostatic pressure). The convective and TissueConnective Ref.'85862.5 10-*1.7 diffusive transport may be in the same direction or in opposite tissue mem braneHuman directions depending upon the pressure and concentration gra aorta-intimamediaHuman x10-*1.3 xIO-62.2 dients. xIO-69x 883x IO'7 87, In what follows we will present published values of each of ilanalÃ¤gearticular i an 10-*6.7 x 10-*89902.8 the transport coefficients, D, K, and RF, for the normal and SalineBrainPlasmaAny xIO'78.75 tumor interstitium. The pressure gradients and convective fluid x10-*3.6 flow in the tumor interstitium were discussed in Section III. tissue*DS-carcinosarcomaTissue x10-*2.6 x IO'7 6691

x10-*4.3 A. Interstitial Diffusion Coefficients slicesAscites cellsGlucose2x x 10-*Inulin Methods. Various methods of measuring diffusion coeffi "Courtesy of P. Vaupel. cients in a (liquid) medium are summarized by Cussler (74). * Estimated using a correlation based on published data. 3045

Downloaded from cancerres.aacrjournals.org on September 29, 2021. © 1987 American Association for Cancer Research. INTERSTITIAL TRANSPORT IN TUMORS where T is the absolute temperature (Â°K= 273+Â°C) during measurement and 77is the viscosity of water. The subscripts of k/6rrÂ¡D0 (G) D and TJrefer to the temperature in "K. Vaupel found that the where k is the Boltzmann constant, and Da is the free diffusion diffusion coefficients of small solutes (O2, CO2, N2, and H2) coefficient of the molecules in water at absolute temperature T decreased exponentially with the percentage of water content, and viscosity y. z, of the tissue: Shown in Fig. 4 are ratios of effective diffusion coefficient to D = a exp(-Ã©z) free diffusion coefficient (D/D0) for sodium fluorescein, BSA, (E) and dextrans versus their Stokes-Einstein radii (94). Note that These results are not surprising since the polysaccharide net in both normal and neoplastic tissues BSA diffusion is signifi work composed of hyaluronate and proteoglycans dispersed in cantly lower than that of a dextran of the equivalent Stokes- the interstitial collagen and elastic fibers offers little resistance Einstein radius. This effect has been observed in several normal to these gaseous molecules. For larger molecules, however, tissues; however, no effects of this nature have been reported hydrodynamic and steric interactions with the solute may be as for diffusion in tumors by other investigators. For example, important as or more important than the water content (see Fox and Wayland (77) found diffusive transport of BSA in the below). rat mesentery to be hindered more than dextrans of the same Molecular Weight Dependence. Diffusion coefficients of mac- molecular size. romolecules, primarily dextrans, in water and in normal tissues The deviation of diffusion coefficients from a strict molecular have been measured by several investigators and can be de size basis could be explained in terms of configuration, charge, scribed by the power law expression (92) and binding of the test molecule. The dextrans used in our study are linear polymers with a slight degree of branching D = a(M,Y (F) (5%), and the albumin molecule is loosely coiled in an ellipso The coefficients a and b for water and various tissues are idal shape in aqueous solution (92, 95). Various in vitro and in summarized in Table 7. Note that the value of the exponent, b, vivo studies have shown greater transport rates of linear mole is ~0.5 for water and ranges from ~0.75 to ~3 for various cules than that of globular molecules of equivalent Stokes- tissues, suggesting that the dependence of the diffusion coeffi Einstein radius (96-98). cients on molecular weight in tissues deviates from that for free Electrostatic repulsion of negatively charged albumin by neg diffusion in water. These results are consistent with the hypoth ative charges of the interstitial matrix would lead to a smaller esis that hydrodynamic and steric interactions among the sol effective volume for diffusion. Works by various investigators ute, solvent, and the interstitial matrix determine the transport on capillary permeability to charged proteins support this hy properties of a solute in tissues, and not just the water content. pothesis as reviewed previously (99, 100). The reduction in D Despite rapid progress in this field, there is a paucity of has been related to the fixed charge density of matrix by interstitial diffusion data in tumors. Nugent and Jain (22) and Maroudas (87). Similarly, the effects of electrochemical poten Gerlowski and Jain (80) obtained the effective interstitial dif tial on interstitial transport in connective tissues have been fusion coefficients of various dextrans and albumin in VX2 reviewed by Grodzinsky (101). carcinoma in vivo (Fig. 3). Note that the macromolecular trans Finally, binding of BSA to the tissue components could port in this tumor is hindered to a lesser extent than in nontu- further reduce the diffusivity of albumin. However, Rutili (102) morous (mature granulation) tissue. Whether this significant found no measurable binding between dextrans and proteins, difference is solely due to the physicochemical characteristics in vivo. The precise role of configuration, charge, and binding of the interstitial matrix of these tissues or due to increased in macromolecular diffusion still needs to be determined for interstitial convection needs to be answered (see below). What normal or neoplastic tissue. ever the cause of this difference is, it favors the use of macro- Pore and Fiber-Matrix Models. The differences between nor molecules in cancer detection and treatment (8, 93). Similar mal and neoplastic tissue diffusion coefficients were related to studies in various animal and human tumors are needed to the size of the solute molecules and to the physicochemical exploit monoclonal antibodies and drug-macromolecule con properties of the interstitial matrix of these tissues using a pore jugates optimally in the management of neoplastic diseases. model and a fiber-matrix model (94, 103). It must be pointed Dependence on Configuration, Charge, and Binding. Since out here that there is little evidence based on electron micro dextrans are linear molecules and albumin is a globular mole graphs that well-defined pores or fiber-matrix structures exist cule, it is more reasonable to compare their transport properties in the interstitial space. However, these two models provide an on the basis of their molecular size than their weight. Usually empirical framework within which to examine the transport the Stokes-Einstein radius, a,. of a molecule is chosen as a relationships of different solutes and to obtain some important measure of its size (92): and useful correlations.

Table 7 Molecular weight dependence of diffusion coefficient in water and tissues

MediumWaterHuman (M,)Dextran 147,000)Dextran(10,000- IO-46.17 xIO"11.778 vitro)Variousarticular cartilage (in (5,000-40.000)Various vitro)Mesenterynormal tissues (in (32-69.000)Dextransolutes xIO-42.75

vivo)CatRatRabbit(HI (3,400-393,000)Dextran xIO"35.5 (3.450-41.200)Dextran xIO"310"2.51 ear (invivo)Mature tissueVX2granulation 50,000)Dextran( 19,400-1 x IO-2b0.4781.340.75(0.65-0.81)0.758Â°1.092.9611.14JRef.928866687722,80 carcinomaSolute (19,400-150,000)aI.26X * Diffusion coefficients are higher in the cat mesentery than in the rat mesentery due to possible diffusion in the superperfusate in the former preparation. 3046 Downloaded from cancerres.aacrjournals.org on September 29, 2021. © 1987 American Association for Cancer Research. INTERSTITIAL TRANSPORT IN TUMORS

100- ably higher compared to measured values of HA. It is possible that collagen fibers also offer resistance to the solute transport (104). Further work is now needed to improve these models to 10- predict diffusion coefficient in tissues based on physicochemical characteristics of solute-tissue system.

B. Hydraulic Conductivity and Retardation Factor Methods. Hydraulic conductivity of tissues is normally ob tained by applying Darcy's law to in vitro filtration data. In o o.H X these experiments, flow rate, (J. of fluid is measured across a o tissue slice of thickness A.r and cross-sectional area/* for known applied pressure difference, Ap, across the tissue. For steady O.OH flow the hydraulic conductivity, K, is given by

(Q/A) K = (H) (Ap/Ax) 0.001 10,000 100,000 200,000 MOLECULAR WEIGHT Extreme care must be exercised during excising, slicing, and holding (clamping) to avoid tissue compression and damage. Fig. 3. Dependence of dextran diffusion coefficients on molecular weight. â€¢. data of Granath and Kvist (92) for aqueous diffusion corrected to 37*C. x, â€¢ Measurement of interstitial K in vivo is extremely difficult. data for VX2 carcinoma and mature granulation tissue, respectively; , best Swabb et ai (66) have measured A of s.c. tissue and Hepatoma fits to the expression a (A/,)* (r2 = 0.999. 0.953, 0.992 for water, tumor, and 5123 in the rat. In these experiments, pressure is suddenly granulation tissue, respectively); bars, SD. Reproduced from the paper of Ger- decreased in a micropore chamber placed in the interstitial lowski and Jain (80). with permission. space, and the resulting flow of interstitial fluid into the cham ber is measured as a function of time. The unsteady state analysis of these data provides the pressure diffusivity, E, which C,-0.6% is equal to K/a0. (Here K is the hydraulic conductivity, a is the interstitial space compressibility, and 6 is the interstitial space volume fraction.) For details, see the paper of Swabb et al. (66). The retardation factor, K,. is normally determined from ultracentrifuge experiments by measuring the ratio of the sedi mentation coefficient of solute in the desired medium to that in physiological saline solution. The interstitial fluid is usually simulated by hyaluronic acid or proteoglycan solutions (105). Results. Hydraulic Conductivity. Hydraulic conductivity, K, of a tissue, similar to that of a porous bed, should depend on tissue interstitial space volume fraction, cell diameter, and 0.001 architecture of the interstitial matrix. In the absence of data on these parameters, Swabb et al. (66) proposed the following RADIUS . nm correlation to describe the in vitro values of K for various tissues Fig. 4. Ratios of effective diffusion coefficient to free diffusion coefficient for sodium fluorescein (Na-F), fiuorescein isothiocyanate (f/7"C)-BSA, and fluores- in terms of their glycosaminoglycan concentration, CGAG(g/ cein isothiocyanate-dextrans versus Stokes-Einstein radius of the molecules; â€¢ 100 g tissue): A. â€¢,tumor; O, A, O, normal tissue: , fiber-matrix model; , pore model; r0, pore radius; CF. fiber concentration. Reproduced from the work of Nugent K = 4.6 x (I) and Jain (94) with permission. These authors estimated tissue GAG content as twice published When the interstitial matrix of a tissue is modeled as a values of hexosamine content for normal tissues, and 0.01-0.05 circular cylindrical pore of radius /â€¢,,.poreradii of 6 and 16 nm, g/100 g for Hepatoma 5123 based on the liver content of 0.088 respectively, describe the dextran data in normal and neoplastic g/100g. tissues adequately. Considerably smaller pore radii (4 nm for Support for this correlation comes from the qualitative stud normal and 6 nm for neoplastic) are required to account for the ies of Day (106,107) and Hedbys (108) who showed an increase restriction of BSA (Fig. 4). in flow across mouse fascia and cornea, respectively, due to the When the tissue interstitial space is modeled as a random application of hyaluronidase. Similarly, Maroudas (109) found matrix of straight fibers of radius rf, fiber concentrations CF of a decrease in tf with increasing fixed charge density of articular 20 and 0.6%, respectively, account for restriction of dextran by cartilage. Note that the fixed charge density is related to GAGs. normal and neoplastic tissues. Considerably higher values of [For more details on the role of polysaccharides on fluid flow, CF (~40% for normal and ~20% for neoplastic) are required to see the reviews by Fatt (110) and Granger (111).] explain the BSA data (Fig. 4). It is of interest to note here that Contrary to the above hypothesis, Jackson and James (112) Fox and Wayland (77) calculated the values of CF to be 6 to found that hyaluronate accounts for only part of the flow 28% to explain their diffusion data for dextran and albumin in resistance. Levick (104) proposes that collagen fibrils can con the mesentery. Our results show that the granulation tissue of tribute significantly to the interstitial resistance due to their the rabbit ear offers a greater restriction to molecular transport volume occupancy and net surface area. The water content, z, than the mesentery. Although the fiber matrix model is in of tissue has been also related to its hydraulic conductivity qualitative agreement with the data, values of CT are consider (109-111). Perhaps one of the most comprehensive power law 3047 Downloaded from cancerres.aacrjournals.org on September 29, 2021. © 1987 American Association for Cancer Research. INTERSTITIAL TRANSPORT IN TUMORS

correlations between K and z was developed by Bert and Fatt (113), which fits K data over 9 orders of magnitude. / f II $'// K = az* (J)

This dependence of K on water content means that during in - Herpes (mommaI) vitro or in vivo experiments water content of a tissue may change â€¢Retorded due to applied pressure and may lead to erroneous results. In transport . Mammary tumor (mouse) 0 KR><0.9 - Adertovtrus (human) this context it is worth noting that K for dog s.c. tissue was found to be about 2 orders of magnitude higher by Guyton et - Poliomyelitis (human) al. (114) than that for rat s.c. tissue found by Swabb et al. (66). (1.8 x IO"9 versus 6.4 x 10~'2 cm4/dyn.s). Similarly, Swabb et SV 60 (primates) al. (66) found K for Hepatoma 5123 about 1 order of magnitude higher in vitro than in vivo (31 x IO"12versus 2.9 - 8.4 x 10~12). DNAt rat mommary gland More in vitro and in vivo studies are needed to resolve the effect Hemoglobin, planorbis of tissue composition on A. IgM Retardation Factor. The relative velocity of a solute with - Complement respect to the solvent velocity, RF, has been studied extensively IgG in model and biological membranes, both experimentally and Albumin theoretically (see, e.g., Ref. 115). There is a paucity of such studies for tissues. The data of Laurent and Pietruszkiewicz (105) on RF in HA solution were described by Swabb et al. (66) by the equation ; - Inulin . - Insulin RF = 1.5 exp[-8.64 x irr3(Mf 3t*(CHA)Â°-5] (K) Actmomycin-0 ThyrOKin for 6.9 x 10" < M, < 2.8 x IO9 and 0 < CHA< 0.35 g/100 g Sucrose Tryptophon solution. Glucose By assuming that tissue has the same retardation properties Glyciiw as the HA solutions, Swabb et al. (66) proposed the following Oxygen empirical correlation after correcting for the interstitial space fraction (0.43): TISSUE GLYCOSAMINOGLYCAN CONTENT RF = 1.5 exp[-1.318 x 10-'(A/r)0366(CcAG)05] (L) g/IOOg WET TISSUE Fig. 5. Importance of diffusive and convective mass transport in the extravas- where CGAGranges from 0 to 0.813 g GAG/100 g tissue. cular space of normal and neoplastic tissue at 37-38*C. The parameter \ is the ratio of solute diffusive flux to convective flux. The position of the lines of More rigorous experimental and theoretical studies along constant X is determined by choosing Ac/(cA/>) = 1/(30 mm Hg), where c is these lines are needed to improve our understanding of convec extravascular solute concentration and p is interstitial fluid hydrostatic pressure. tive transport of solute in the interstitium. The retardation factor K, is the solute convective flow velocity/solvent convective flow velocity for flow through a polysaccharide network. Published data validating the analysis are: â€¢,mouse mammary adenocarcinoma BICR/SA1 and human bronchial carcinoma (116, !!");â€¢, mouse mammary tumors C3HBA (65, 118); C. Ratio of Convection versus Diffusion in the Interstitium A, Walker carcinoma 256 (119); O, dog paw (120); D, ox corneal siroma (121); A, human articular cartilage (122). Indicated tumor glycosaminoglycan contents Despite overwhelming evidence for significant interstitial are approximate. Reproduced from Swabb .â€¢/al.(66) with permission. convection in normal and neoplastic tissues, there is no direct measurement of the magnitude and direction of convective The analysis of Swabb et al. (66) assumes that diffusion and velocity of a solute or solvent in the interstitium (see Section convection occur in the same direction making X > 0. If these III). In the absence of such hard data one can only hypothesize processes occur in the opposite direction X would be negative. about the relative contribution of convection to the interstitial In addition, due to spatial heterogeneity in the interstitial transport. For one dimensional transport, using Equations B pressure, solute concentration, interstitial volume fraction, pol and C, one can obtain ysaccharide concentration, charge distribution, binding, fluid Diffusive flux D AC _)_ viscosity, and tissue hydration, X may differ from one location X = (M) Convective flux RF* C Ap to another in the tissue. The need for experimental and theo retical investigations to address these issues is urgent. in which Xis JD/JC (flux ratio). To obtain an order of magnitude of X, Swabb et al. (66) assumed AC/C ~ 1 and Ap -30 mm Hg and simplified Equation M to V. Conclusions and Future Perspective X = 2.5 x IO'5 D/RfK (N) The objective of this review article was to summarize our current understanding of transport of fluid and solute molecules Using the empirical correlations for D (Table 7), K (Equation in the tumor interstitium. To this end, we have discussed various I), and RF (Equation L), these authors estimated diffusion to experimental and theoretical approaches to quantify interstitial convection ratios for solutes of given molecular weights moving transport in tissues. The data available in the literature suggest through tissues with known GAG content (Fig. 5). Note that that the tumor interstitium is significantly different in structure the transport of low molecular weight substances is diffusion and function from the interstitium of most normal tissues. In dominated while convection becomes important at higher mo general, the tumor interstitial compartment is characterized by lecular weights. a large interstitial space, high collagen content, low proteogly- 3048 Downloaded from cancerres.aacrjournals.org on September 29, 2021. © 1987 American Association for Cancer Research. INTERSTITIAL TRANSPORT IN TUMORS

4. Jain, R. K. Mass and heat transfer in tumors. Adv. Transport Process, *: can and hyaluronate concentrations, and absence of anatomi 205-339, 1984. cally well-defined functioning lymphatic network compared to 5. Covell, D. G., Barbel, J., Holton, O. D., Black, C. D. V., Parker, R. J., and Weinstein, J. N. Pharmacokinetics of monoclonal immunoglobin (.,. most normal tissues. These structural differences are presum F(ab')2. and Fab' in mice. Cancer Res., 46: 3969-3978, 1986. ably responsible for high interstitial fluid pressure and bulk 6. Schlom, J. Basic principles and applications of monoclonal antibodies in fluid flow and high effective interstitial diffusion coefficient of the management of carcinomas. Cancer Res., 46: 3225-3238, 1986. macromolecules as well as large hydraulic conductivity in tu 7. Winkler, C. (ed.). Nuclear Medicine in Clinical Oncology. Berlin: Springer- Verlag, 1986. mors. 8. Jain, R. K. Transport of macromolecules in tumor microcirculation. Bio- Despite rapid progress in this area in recent years, there is a technol. Prog., /: 81-84, 1985. paucity of quantitative data on interstitial transport parameters 9. Jain, R. K., and Ward-Hartley, K. Tumor blood flow: characterization, modifications, and role in hyperthermia. I.E.E.E. Trans. Sonics Ultrasonics, in tissues and several questions remain unanswered. Through SU-31: 504-526, 1984. out the text, these unresolved problems were pointed out in 10. Balazs, E. A. (ed.). Chemistry and Biology of Intercellular Matrix, Vols. 1, 2, and 3. New York: Academic Press, 1970. hopes of stimulating multidisciplinary research in this area. In 11. Viidik, A., and Vuust, J. (eds.). Biology of Collagen. New York: Academic what follows, some of these problems are summarized. Press, 1980. Despite the overwhelming evidence and importance of in 12. Aukland, K., and Nicolaysen, G. Interstitial fluid volume: local regulatory mechanisms. Physiol. Rev., 61: 556-698. 1970. creased interstitial convection in tumors, there are no direct 13. Hargens, A. R. (ed.). Tissue Fluid Pressure and Composition. Baltimore: measurements of magnitude and/or direction of convective Williams & Wilkins, 1981. velocity in normal and tumor tissues. Recent development in 14. Hay, E. D. (ed.). Cell Biology of Extracellular Matrix. New York: Plenum Publishing Corp.. 1981. fluorescent microscopy should permit measurements of convec 15. Bert, J. L.. and Pearce, R. H. The interstitium and microvascular exchange. tive versus diffusive transport in the interstitium. Availability In: E. M. Renkin and C. C. Michel (eds.). Handbook of Physiologyâ€”The of such information would help in determining optimal size of Cardiovascular System, Vol. 4, Chap. 12, pp. 521-547. Bethesda, MD: American Physiological Society, 1984. macromolecules for tumor detection and treatment. 16. Gullino, P. M. Extracellular compartments of solid tumors. In: F. F. 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